Multiplicity dependence of K*(892)0 and ϕ(1020) production in pp collisions at s=13 TeV

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Multiplicity

dependence

of

K*(892)

0

and

φ

(1020)

production

in

pp

collisions

at

√

s

=

13 TeV

.

ALICE

Collaboration



a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received13December2019

Receivedinrevisedform25March2020 Accepted18May2020

Availableonline28May2020 Editor:L.Rolandi

Thestrikingsimilaritiesthathavebeenobservedbetweenhigh-multiplicityproton-proton(pp)collisions and heavy-ion collisions can be exploredthrough multiplicity-differentialmeasurements of identified hadronsinppcollisions.Withthesemeasurements,itispossibletostudymechanismssuchascollective flow that determine the shapesofhadron transverse momentum(pT) spectra, to searchfor possible

modificationsoftheyieldsofshort-livedhadronicresonancesduetoscatteringeffectsinanextended hadron-gasphase, and to investigatedifferentexplanations providedby phenomenologicalmodels for enhancement of strangeness production with increasing multiplicity. In this paper, these topics are addressedthroughmeasurements oftheK∗(892)0_{and φ(1020)mesonsatmidrapidityinppcollisions}

at√s₌ 13 TeVas afunctionofthe charged-particlemultiplicity. Theresults includethe pTspectra,

pT-integratedyields,meantransversemomenta,andtheratiosoftheyieldsoftheseresonancestothose

oflonger-livedhadrons.Comparisonswithresultsfromothercollisionsystemsandenergies,aswellas predictionsfromphenomenologicalmodels,arealsodiscussed.

©2020EuropeanOrganizationforNuclearResearch.PublishedbyElsevierB.V.Thisisanopenaccess articleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

1. Introduction

Recent studies of proton-proton (pp) and proton-lead (p–Pb) collisionsattheLHCwithhighcharged-particlemultiplicitieshave shown patterns of behavior that are reminiscent of phenomena observedinheavy nucleus-nucleus(A–A)collisionssuchasPb–Pb andXe–Xe.Thesystems createdinthesecollisions are compared by classifyingevents accordingto the final-statecharged-particle multiplicity,which is used asa measure of the “activity” of the event.In smallcollision systemssuch aspp andp–Pb, multiplic-ities range from a few to a few tens of charged particles per unit of rapidity, whereas in large systems (A–A collisions), mul-tiplicities of a few thousand chargedparticles per unit of rapid-ity can be produced. As discussed below, measurements of az-imuthal anisotropies in particle emission [1–7] (quantified using theFouriercoefficientsofazimuthaldistributionsofproduced par-ticles),themultiplicityevolutionofhadron pTspectra [8–11],and pT-differential baryon-to-meson ratios suggest the possibility of

collectiveflow even in smallsystems. Furthermore,the observed enhancementofstrangehadron production [8,9,12] couldindicate the productionof a quark–gluon plasma (QGP), while the possi-blesuppressionoftheyieldsofshort-livedresonances [8,11] may suggestthe presenceof an extendedhadronic phase.However, it remainsanopenquestionwhethertheunderlyingcausesofthese behaviorsaretrulythesameinsmallandlargecollisionsystems.

 _{E-mailaddress:alice-publications@cern.ch.}

In order to investigatethis, the ALICE Collaborationhas mea-sured the pT spectra and total yields of identified hadrons asa

function ofthe charged-particle multiplicity inp–Pb collisions at

√

sNN

=

5.02 TeV [10,11,13–15] andpp collisions at

√

s

=

7 TeV

[8,12,16] for many species, including

π

±, K±, K0_S, K∗

(

892

)

0, p,

φ(

1020

)

,



,



−,



−,deuterons, andtheir antiparticles.This pa-per reportson an extension of these studies: a measurement of themultiplicityevolutionoftheproductionofK∗

(

892

)

0,K∗

(

892

)

0, and

φ(

1020

)

mesons inpp collisions at

√

s

=

13 TeV,the high-estenergyreachedbytheLHCinruns1and2.Thepresentstudy takesadvantageofappdatasetrecordedduringRun2oftheLHC in2015withan integratedluminosity of0.88 nb−1 and comple-mentsotherrecentALICEpapersonlight-flavorhadronproduction inthe samecollision system, bothin inelasticcollisions [17] and asafunction ofcharged-particlemultiplicity [9,18,19].Forthe re-mainder ofthispaper,the averageofK∗

(

892

)

0 andK∗

(

892

)

0 will bedenotedasK∗0,whilethe

φ(

1020

)

willbedenotedas

φ

.

The ratios of the yields ofstrange hadronsto pion yields are observed to be enhanced in A–A collisions relative to minimum biasppcollisions [20–22],withtheyieldsincentralA–Acollisions beingwelldescribedbystatisticalthermalmodels [23–26].In cen-tral A–A collisions, strangeness is produced from the hadroniza-tion of a strangeness-saturated QGP andthe relative abundances of hadrons reflect the degree of equilibration of the system. At theLHC,hadron-to-pionyieldratiosareobservedtoincreasewith thecharged-particlemultiplicityinppandp–Pbcollisions [8–13]; the magnitude of the change from low to high multiplicity

in-https://doi.org/10.1016/j.physletb.2020.135501

0370-2693/©2020EuropeanOrganizationforNuclearResearch.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

creases with the strangeness content of the hadron. The ratios in high-multiplicity pp andp–Pb collisions reach the values ob-served inperipheralPb–Pb collisionsandgenerallyfollowsimilar trends as the multiplicity increases frompp to p–A to A–A col-lisions.Furthermore,the yields ofstrange particlesare consistent between

√

s

=

7 and 13 TeV for similar charged-particle multi-plicities. These results suggest that the yields of these hadrons dependprimarily on thecharged-particle multiplicity andare in-dependent of the collision system and energy. This is perhaps a surprising result: pp, p–Pb, and A–A collisions involve different physicalprocesses(e.g.differentcontributions fromjetsand mul-tiplepartonic interactions)andproduce pT spectrawithdifferent

shapes. Nevertheless, the total abundances of hadrons, even rare particles like



− and light nuclei, are consistent across the dif-ferent collision systems for a given charged-particle multiplicity, suggestingthattheremaybesomeunderlyingsimilaritiesbetween thedifferentcollisionsystems.Comparisonsofthesedifferent col-lision systems atsimilar multiplicities may, forexample, help to addressthequestion ofwhetheraQGPmightbe presenteven in high-multiplicityppandp–Pbcollisions,oralternatively, whether non-QGPeffectsmightexplainbehaviorseeninA–Acollisions.

Several theoretical explanations of the multiplicity evolution of strange-hadron production have been put forward, including canonicalsuppression,ropehadronization,andcore-coronaeffects. Instatisticalthermalmodelsoflargecollisionsystems,strangeness productionisdescribed throughthe useofagrandcanonical en-semble, where strangeness conservation is realized on average acrossthevolumeofthesystem.Inthecanonicalsuppression pic-ture,strangenessproductioninsmallsystemsisinsteaddescribed using a canonical ensemble, requiring the exact local conserva-tionofstrangenesswithinthesmallvolume [8,27,28].Asthesize of the system decreases, it makes a transition from the grand-canonical to the canonical description, leading to a decrease in strange-hadron yields with decreasing multiplicity. In the rope-hadronizationpicture,thelargeranddensercollisionsystemsform colorropes [29–31],groups ofoverlapping stringsthat hadronize witha largereffectivestring tension.Thiseffect,implementedin modelssuchasDIPSY [32–34],alsoleadstoanincreaseinthe pro-duction ofstrange hadronswithincreasing charged-particle mul-tiplicity. Core-corona separation is implemented in a variety of models, including EPOS [35–38] and those described in [39,40]. In these models, the collision is divided into “core” and “coron-a” regions, with the division determined by the string or parton density. Regions with a density greater than the threshold den-sitybecomethecore,whichmayevolveasaquark–gluonplasma. This is surroundedby a more dilute corona, for which fragmen-tationoccursas inthe vacuum. Strangeness productionis higher inthecoreregion, whichmakes upa greaterfractionofthe vol-umeofthelargercollisionsystems.Thisalsoresultsinstrangeness enhancementwithincreasingmultiplicity.

The

φ

meson is a useful probe for the study of strangeness enhancement. The

φ

contains two strange valence (anti)quarks, buthasnonetstrangeness.Its productionshouldthereforenotbe canonicallysuppressed,whiletheproductionofhadronswithopen strangeness(e.g. kaons or



) maybe canonically suppressed [8]. It has, in fact, been rather difficult to describe enhancement of

φ

-mesonproductioninaframework that involvescanonical sup-pression [8].Incontrast,intherope-hadronizationorcore-corona interpretations, the yields of

φ

mesons evolve with multiplicity similarlytoparticleswithopenstrangeness,leadingtoanexpected increase in the pT-integrated

φ

/

π

ratio withincreasing

charged-particle multiplicity. Measurements of

φ

-meson production as a function ofthe multiplicity mayhelp to distinguish betweenthe variousexplanationsofstrangenessenhancementinsmallsystems. One ofthe mainmotivations forstudying resonances likeK∗0

and

φ

in heavy-ion collisions is to learn more about the

prop-erties (temperature and lifetime) of the hadronic phase of the collision. Whenshort-lived resonances(suchas

ρ(

770

)

0_,K∗0_,and

(

1520

)

) decay, their daughters may re-scatter in the hadronic phase,leading toareductioninthemeasurableresonanceyields; conversely, resonances may also be regenerated due to quasi-elastic scattering of hadrons through a resonance state [41–46]. Centrality-dependent suppression of

ρ(

770

)

0, K∗0, and

(

1520

)

production was observed in Pb–Pb collisions [47–50], anda hint of K∗0 suppression was reported forp–Pb collisions [11]. Obser-vations ofa similar suppressionin high-multiplicitypp collisions (e.g.,theK∗0

_/

_{K ratioinppcollisions at}

√

_s

₌

_{7 TeV [8])mightbe}

anindication forahadronicphasewithnon-zerolifetimein high-multiplicityppcollisions.

Measurementsofidentifiedhadronscanalsobe usedtostudy collective motion in A–A collisions and to search for similar ef-fectsinsmallcollision systems.Innon-centralA–Acollisions, the initialspatial anisotropyintheoverlapregion ofthecolliding nu-clei results in azimuthally anisotropic pressure gradients in the produced medium, leading to azimuthal anisotropies in particle emission.Thisanisotropicflowisamanifestationofhydrodynamic behavior in theQGPproduced in theA–Acollision system. Mea-surements of azimuthal correlations and anisotropies in particle emission [1–7] alsosuggest thepossibilityofcollectivemotionin smallcollisionsystems.Itwasobservedthattheslopes ofhadron

pT spectra increase with increasing multiplicity in pp and p–Pb

collisions [8–11],whileanenhancementin pT-differential

baryon-to-mesonratios(e.g.p/

π

and



/K0

S)isobservedatintermediate pT

(2



pT



7 GeV

/

c).Thisisatleastqualitativelysimilartothe

be-haviorobservedinPb–Pbcollisions [51–54],wheretheeffectscan be attributedto a collective expansion of thesystem. In this in-terpretation, hadronsreceive amomentum boost inthedirection transverse to the beamaxis, which increases in magnitudewith increasing multiplicity andislargerformoremassiveparticles. It shouldbenoted,however,thatothereffects,including recombina-tion [55–57], may be able to account forthe observed behavior. TheincreaseintheslopesofthepT spectraisalsomirroredinthe

trendofthemeasuredmeantransversemomenta



pT.Incontrast to theyields, whichevolve along a continuous trendwith multi-plicityacross differentcollision systems,the



pTvaluesof light-flavorhadronsfollowdifferenttrendsinpp,p–Pb,andPb–Pb col-lisions [10–12,51],witha fasterincrease forthe smallersystems. The



pTvaluesinthe highestmultiplicitypp collisions reach,or in some casesexceed, the



pT values observedin central Pb–Pb collisions. The increase in



pT inpp collisions isdueto changes inthe shapesofthe pT spectra atlow pT; for pT



4 GeV

/

c,the

shapes ofhadron pT spectra are essentially independent of

mul-tiplicity [9,58]. The color reconnection (CR) mechanism [59–63] describes the interconnections and interactions between strings that originate from different multi-parton interactions. It is im-plementedinvariousforms,sometimesincludingtheformationof colorropes, inseveraleventgenerators basedon string fragmen-tation. Color reconnection can also modify the yields of hadron species(e.g.increasingtherateofbaryonformation)andcanlead to collectiveflow-like effects,eveninsmallcollision systemsand ineventgeneratorslikePYTHIAthatdonotincludeQGPformation. The results reported here will allow the study of K∗0 and

φ

productionasfunctionsofbothenergyandmultiplicityinpp col-lisions. The presented results reach higher values of multiplicity than previously measured in pp collisions and therefore provide importantadditionalinformationontheproductionoflight-flavor hadrons atLHC energies. This paperis organized asfollows. The ALICEdetectorandthecriteriaadoptedfordataselectionare de-scribedinSection2.Asummaryofthedataanalysisprocedureis giveninSection3.Theresultsarepresentedanddiscussedin Sec-tion4,followedbyasummaryandconclusionsinSection5.

Table 1

Charged-particle multiplicity densities at midrapidity dNch/ dη|η|<0.5 for the INEL>0 class and the various V0M multiplicityclasses [9]. Class dNch/dη|η|<0.5 INEL>0 6.89±0.11 I 25.75±0.40 II 19.83±0.30 III 16.12±0.24 IV 13.76±0.21 V 12.06±0.18 VI 10.11±0.15 VII 8.07±0.12 VIII 6.48±0.10 IX 4.64±0.07 X 2.52±0.04

2. Event and track selection

The ALICEdetector is described in detail in [64,65]. The sub-detectorsthatare relevanttotheanalysisdescribed inthispaper aretheTimeProjectionChamber(TPC),theTime-of-Flightdetector (TOF),the Inner TrackingSystem(ITS), the V0detectors, andthe T0detectors.TheTPCandITSareusedfortrackingandfindingthe primaryvertex,whiletheTPCandTOFareusedforparticle identi-fication.TheV0detectors(scintillatorarrays)andtheT0detectors (arrays ofCherenkov counters) sit on eitherside ofthe nominal centerofthe detectoratsmall angleswith respectto the beam-line. The V0 detectors are used for triggering and to define the multiplicityestimatoratforwardrapidities(pseudorapidityranges

−

3

.

7

<

η

<

−

1

.

7 and2

.

8

<

η

<

5

.

1).TheT0detectorsprovide tim-inginformation,includingastartsignalfortheTOF.

The K∗0 and

φ

mesons are reconstructed from a sample of 5

×

107 ppcollisionsat

√

s

=

13 TeVrecordedin2015.The mini-mumbiastriggerrequiredhitsinbothV0detectorsincoincidence withprotonbunchesarrivingfrombothdirections.Beam-induced backgroundandpile-upeventsare removedoffline; see [9,65] for details.Selected eventsmustalsohavea primary collisionvertex reconstructed with the two innermost layers of the ITS and lo-catedwithin

±

10 cmalongthebeamaxisofthenominalcenterof theALICEdetector.Resultsinthispaperarepresentedfordifferent eventclassescorrespondingtosubdivisionsofthe“INEL

>

0”event class,whichisdefinedasthesetofinelasticcollisionswithatleast onechargedparticleintherange

|

η

|

<

1 [66]. TheINEL

>

0 sam-ple isdivided intomultiplicity classes based on the total charge depositedinbothV0detectors(calledthe“V0Mamplitude”).Thus, theeventclassesaredeterminedbythenumberofcharged parti-clesatforwardrapidities,whiletheK∗0_and

_φ

_{yieldsaremeasured}

at midrapidity

(

|

y

|

<

0

.

5

)

; this is to avoid correlations between theK∗0and

φ

yieldsandthemultiplicityestimator.Particleyields, yieldratios,andmeantransversemomentaareplottedfordifferent multiplicity classes(whichcorrespond todifferent centralitiesfor A–Acollisions)asfunctionsofthecorrectedmeancharged-particle multiplicitydensityatmidrapidity



dNch

/

d

η



|η|<0.5,where

η

isthe

pseudorapidityinthelabframe.Asin [9],thevariousmultiplicity classesare denoted usingRoman numerals, with classI (X) hav-ingthehighest(lowest)multiplicity.SeeTable1forthevaluesof



dNch

/

d

η



|η|<0.5 measuredforeachV0Mmultiplicityclass.

SincetheK∗0and

φ

mesonsareshort-lived(i.e.,theirlifetimes areofthe orderof

∼

10−23 sandtheir decay verticescannot be distinguished from the primary collision vertex), they cannot be measureddirectlybythedetector.Instead,they arereconstructed viatheirhadronicdecaystochargedpionsandkaons:K∗0

→ π

±K∓ (branchingratio66

.

503

±

0

.

014%) and

φ

→

K+K− (branching ra-tio 49

.

2

±

0

.

5%) [67]. Charged tracks are selected using a set of standard track-quality criteria, described in detail in [11]. Pions

andkaons are identified usingthe specificionization energy loss dE

/

dx measured in theTPC andthe flight time measured inthe TOF.WherethedE

/

dx resolutionoftheTPCisdenotedas

σ

TPC,

pi-ons andkaonsare requiredtohavedE

/

dx valueswithin 2

σ

TPC of

theexpectedvaluefor p

>

0

.

4 GeV

/

c,within4

σ

TPC for0

.

3

<

p

<

0

.

4 GeV

/

c,andwithin 6

σ

TPCfor p

<

0

.

3 GeV

/

c (typically,

σ

TPC

∼

5% of the measured dE

/

dx value). When a pion orkaon track is matchedtoahitintheTOF,thetime-of-flightvalueisrequiredto be within3

σ

TOF oftheexpectedvalue (

σ

TOF

∼

80 ps) [68]. These

event- andtrack-selectioncriteriaarevariedfromtheirdefault val-uesandthe resultingchanges inthe yields areincorporated into thesystematicuncertainties,whicharesummarizedinTable2.

3. Data analysis

The K∗0 _and

_φ

_{signals are extracted using the same}

invari-antmassreconstructionmethoddescribed in [11,17,48].Invariant mass distributions of unlike-charge

π

K or KK pairs in the same event are reconstructed after particle identification. The combi-natorial background is estimated usingmultiple methods. In the “like-charge” method, tracks of identical charge from the same eventarecombinedtoformpairs.Thisbackgroundis2

√

n₋₋n₊₊, where n₋₋ and n₊₊ are the number of negative-negative and positive-positive pairs in each invariant mass bin, respectively. In the “mixed-event” method, tracks from one event are com-bined with oppositely charged tracks fromup to 5 other events withsimilarprimaryvertexpositionsandmultiplicitypercentiles. Specifically, it is required that the longitudinal positions of the primaryverticesdifferbylessthan1 cmandthemultiplicity per-centiles computed using the V0M amplitude differ by less than 5%. The mixed-event

π

K (KK) background is normalized so that it has the same integral as the unlike-charge same-event dis-tribution in the invariant mass range 1

.

1

<

mπK

<

1

.

15 GeV

/

c2

(1

.

05

<

mKK

<

1

.

08 GeV

/

c2). In evaluating the systematic

uncer-tainties,theboundariesofthenormalizationregionforthe mixed-eventbackgroundarevariedby

∼

100 MeV

/

c2 _fortheK∗0_analysis

and

∼

10 MeV

/

c2 _for

_φ

_.

After subtraction ofthe combinatorial background,the invari-ant mass distribution consists of a resonance peak sitting on top of a residual background of correlated pairs. This correlated backgroundcontains contributions fromjets, resonancedecays in which a daughter is misidentified, and decays with more than two daughters. In the analysis of the

φ

meson in pp collisions, thesignal-to-background ratioislarge andthe backgroundis ob-servedtovaryslowly intheregionofthepeak.Forthesereasons, athirdapproachisalsousedtodescribethebackgroundinthe

φ

analysis;thecombinatorialbackgroundisnotsubtracted,butis in-stead parameterizedtogether withthe residualbackground using afunctionasdescribedbelow.Thishastheadvantageofproviding smallerstatisticaluncertaintiesthantheothermethods.

For pT

<

4 GeV

/

c,all threemethodsprovidegooddescriptions

ofthe KK backgroundandgive

φ

yields within a fewpercent of each other.The final

φ

yields for pT

<

4 GeV

/

c are theaverages

ofthoseextractedusingthethreemethodsofdescribingthe com-binatorialbackground,whilethespreadamongtheresultsforthe differentmethodsisincorporatedintothesystematicuncertainties. As pT increases, the yields of hadrons decrease, along with the

magnitudes of all of the combinatorialbackgrounds studied. The mixed-event background,which lacks anycontribution from cor-relatedpairs,isobservedtobecome smallerthanthesame-event (like- orunlike-charge)combinatorialbackgroundsaspTincreases,

eventuallytending to0forpT valueshigherthantheranges

con-sidered here. While the mixed-event background could still be usedforthe

φ

analysisfor4

≤

pT

≤

8 GeV

/

c,thetwoother

tech-niques havesmaller statisticalfluctuationsinthis pT range.

Table 2

Sources ofsystematic uncertaintiesfor the pT spectraof K∗0 and φ reported for low,intermediate,and high pT. Whenonlyone valueis givenforone par-ticle,the uncertaintydoesnotdependon pT. “Signalextraction”includes varia-tionsofthecombinatorial background,mixed-eventnormalizationregion, fitting region,peakshape,andresidualbackgroundfunction.The“signal-loss”uncertainty ismultiplicity-dependent,hencevaluesarequotedforthehighestandlowest mul-tiplicityclasses(IandX,respectively).Thetext“negl.”indicatesanegligible uncer-taintyand“had.int.crosssec.”isshortfor“hadronicinteractioncrosssection.”

Particle pT(GeV/c) K∗0 _φ 0.2 2.2 6.5 0.7 2 6 event/track selection 4.3% 1.6% 2.9% 2.7% 2.9% 3.2% signal extraction 10.3% 6.7% 7.7% 2.7% 3.1% 3.1% ITS-TPC matching 2.0% 2.0%

branching ratio negl. 1.0%

material budget 2.0% 0.5% negl. 5.3% 1.0% negl. had. int. cross sec. 2.6% 1.2% negl. 2.1% 2.6% negl.

signal loss, class I negl. negl.

signal loss, class X 3.9% 2.4% 0.9% 2.3% 4.8% 2.2%

of

φ

for pT

>

4 GeV

/

c.Themixed-eventtechniqueistheprimary

methodusedfortheextractionoftheK∗0 yields;variationsofthe yieldduetotheuseofalike-chargebackgroundarecoveredbythe systematicuncertainties.However,forpT

<

0

.

8 GeV

/

c in

multiplic-ityclassI, thelike-chargemethodispreferred,sinceitprovidesa betterdescriptionofthebackground.Athigh pT,themixed-event

backgroundfortheK∗0 _{analysisexhibitsthesamebehaviorasfor}

the

φ

,buttheproblemsappearathigherpTvaluesthanfor

φ

.The

mixed-eventtechniquethereforeremainsthebestavailableoption forthisK∗0 _{analysis,evenatthehighendofthep}

T rangethatwas

studied.

The invariant mass distributions are fitted with a peak func-tionaddedtoasmoothresidualbackgroundfunction.ForK∗0_,the

peak is described using a Breit-Wigner function. The mass reso-lutionof thedetectorfor the

φ

→

K−K+ channel isof thesame orderofmagnitudeasthe

φ

width.Therefore, the

φ

peak is de-scribed using a Voigt function: a convolution of a Breit-Wigner functionandaGaussianwhichaccountsforthemassresolutionof thedetector.TheK∗0 and

φ

widthparametersarebydefaultfixed to their vacuumvalues;to calculatethe systematicuncertainties, theseparametersare allowed tovaryfreely andthe

φ

resolution parameteris fixedto thevalues(approximately 1–2 MeV

/

c2) ex-tracted from the Monte Carlo simulations described below. The residual backgroundis parameterized usinga second-order poly-nomial.ToevaluatethesystematicuncertaintiesintheK∗0 yields, athird-orderpolynomialisusedinstead.Forthe

φ

systematic un-certainties, a first-order polynomial and a function of the form

A

+

BmKK

+

C



mKK

−

2M

(

K±

)

are used. Here, A, B, and C are

free parameters, mKK is the kaon-kaon pair invariant mass, and M

(

K±

)

isthemassoftheK±.Thefitsareperformedinthe invari-antmassintervals0

.

75

<

mπK

<

1

.

07 GeV

/

c2 fortheK∗0 analysis

and0

.

995

<

mKK

<

1

.

09 GeV

/

c2 forthe

φ

. Theranges ofthefits

are variedby

∼

20 MeV

/

c2 _forK∗0 _and

_∼

_{10 MeV}

_/

_c2 _for

_φ

_;the

resultingchangesintheyieldsare includedinthesystematic un-certainties.Finally,particleyields areextractedby integratingthe invariant mass distribution in the peak region (0

.

798

≤

mπK

≤

0

.

994 GeV

/

c2 _forK∗0 _and1

_.

₀₁

_≤

_m

KK

≤

1

.

03 GeV

/

c2 for

φ

),

sub-tractingtheintegraloftheresidualbackgroundfunctionunderthe peak,andaddingtheyieldsinthetailsofthepeakfitfunction out-sidetheintegrationregion.Thesystematicuncertaintyarisingfrom “signal-extraction”, as quoted in Table 2, covers the aforemen-tioned variations in the combinatorial background, mixed-event normalizationregion,residualbackgroundfunction,peakfunction, andfitrange.Anadditionaluncertaintyoriginatesfromthe proce-dure usedto matchtracksegments in theITSwithtracks inthe TPC.Thebranchingratiocorrectionforthe

φ

yieldintroducesa1% uncertainty,whilethecorrespondinguncertaintyforK∗0_is

negligi-ble.Uncertaintiesintheyieldsduetouncertaintiesinthematerial budgetofthedetectorandthecrosssectionsforhadronic interac-tionsinthatmaterialaretakenfromapreviousstudy [11].

The raw particle yields are corrected for the branching ra-tios, aswell as the acceptance and efficiency of the reconstruc-tion procedure. The correction for acceptanceand efficiency (de-noted as A

×

ε

) is calculated using several different event gen-erators (PYTHIA6Perugia 2011 tune [69],PYTHIA8 Monash2013 tune [70],andEPOS-LHC [38]),withparticlespropagated through a simulation ofthe detector using GEANT3 [71]. No dependence on thegeneratorisobservedandtheaverage A

×

ε

forthethree generators is usedin orderto reduce statisticalfluctuations. This correction isofthesameorderasreportedin [11].Adependence on multiplicity is observed; for pT

<

3 GeV

/

c, A

×

ε

increases

by

∼

10% from multiplicity class I to class X. In the calculation of A

×

ε

, a weighting procedure is used to account forthe fact that (1) A

×

ε

may varysignificantly overthe widthof a pT bin

inthe measuredspectrum and(2)thesimulated pT distributions

usedinthecalculationdonotnecessarilyhavethesameshapesas themeasuredpT distributions.IntheMonteCarlosimulations,the

generatedandreconstructed pT spectra(thedenominatorand

nu-merator inthe A

×

ε

calculation, respectively) areconstructed in narrow pT binsandthenweightedusingafitofthemeasured pT

spectra.Thesimulated pT spectraafterthisweightingareusedto

recalculate A

×

ε

in thewider pT binsusedforthemeasured pT

spectra.Thisprocedure (alsoused in [8,9,47,48,50] andothers) is repeateduntilthe changesinthe correctionfactorbecome negli-giblebetweeniterations;nomorethanthreeiterationsareneeded fortheprocesstoconverge.

A “signal-loss” correction is also applied, which accounts for K∗0 and

φ

mesonsinnon-triggeredevents.Thisisevaluatedusing the same simulations as the acceptanceand efficiency. To calcu-late this correction factor, the simulated resonance pT spectrum

beforetriggeringandeventselectionisdividedbythe correspond-ing pT spectrumafterthose selectionsforeach multiplicity class.

The signal-loss correction typically deviates from unity by

<

1%, but can deviate by

∼

10% at low pT forthe lowest multiplicity

class. Different event generators provide different descriptions of the non-triggered component of the various multiplicity classes. Following [9], thePYTHIA6simulation isused toobtain the cen-tral values for this correction, while an uncertainty is evaluated by comparing the central values to those givenby PYTHIA8and EPOS-LHC. Finally, the pT spectraare normalizedby the number

ofacceptedeventsandcorrectedasin [9] toaccountforINEL

>

0 events that do not pass the event-selection criteria. This correc-tion, which is calculated using the PYTHIA6 simulation, is most important (24%) forthelowest multiplicity class andis

<

1%for high-multiplicitycollisions(classesI-VIII).

4. Results

The pTspectraforK∗0and

φ

inthevariousmultiplicityclasses,

aswellastheratiosofthesespectratotheinclusiveINEL

>

0 spec-trum, are shownin Fig.1. For pT



4 GeV

/

c the increase in the

slopes of the pT spectra from low to high multiplicity is clearly

visible.Forhigher pT,thespectra indifferentmultiplicity classes

allhavethesameshape,indicatingthattheprocessesthatchange the shape of the pT spectra in different multiplicity classes are

dominantprimarilyatlow pT.A similarbehaviorwasreportedfor

unidentifiedchargedhadrons,K0_S,



,



,and



forthesame colli-sionsystem [9,58].

The pT-integratedyieldsdN

/

d y andmeantransversemomenta



pTareextractedfromthe pTspectrainthedifferentmultiplicity

classes.For eachmultiplicity class, the

φ

yieldis extrapolatedto the unmeasuredregion (pT

<

0

.

5 GeV

/

c) by fitting a Lévy-Tsallis

Fig. 1. pTspectraofK∗0andφinppcollisionsat√s=13 TeVfordifferentmultiplicityclasses,scaledbyfactorsasindicated.Thelowerpanelsshowtheratiosofthe multiplicity-dependentpTspectratothemultiplicity-integratedINEL>0 spectra(withbothlinearandlogarithmicverticalscales).

Fig. 2. Mean transversemomentapTofK∗0_{andφasfunctionsofdN}

ch/ dη|η|<0.5.Resultsareshownforppcollisionsat√s=13and7 TeV [8],aswellasforp–Pb collisionsat √sNN=5.02 TeV [11].Themeasurementsinppcollisionsat √s=13 TeVarealsocomparedtovaluesfromcommoneventgenerators [33,38,69,70].Bars representstatisticaluncertainties,openboxesrepresenttotalsystematicuncertainties,andshadedboxesshowthesystematicuncertaintiesthatareuncorrelatedbetween multiplicityclasses(negligibleforp–Pb).

I(X)the extrapolated

φ

yield is12%(34%)ofthe totalyield.The K∗0 is measured down to pT

=

0 and no low-pT extrapolationis

neededtocalculatedN

/

d y forthatparticle.Theextrapolatedyield athighpTisnegligibleforbothparticles.The



pTisevaluated

us-ingthemeanvalueofthefitfunctionwithineachpTbin,weighted

bythemeasuredyieldineach bin.For

φ

,thefitfunctionisused to calculate the yield and mean pT in the low-pT extrapolation

region,but thisisnot needed forK∗0_{. The sources of systematic}

uncertaintyforthepTspectraalsocontributetothesystematic

un-certaintiesofdN

/

d y and



pT,exceptfortheITS-TPCmatchingand branching ratio uncertainties, which are pT-independent and do

not contribute to theuncertainties ofthe



pTvalues. Additional uncertaintiesindN

/

d y and



pTof

φ

areevaluatedbyvaryingthe fitrangeandtheformoftheextrapolationfunction:Bose-Einstein, Boltzmann,andBoltzmann-Gibbsblast-wave [75] distributions,as wellasanexponentialinmT(wheremT

≡



M2

₊

_p2

T

/

c2andM is

themassoftheparticle).Theuncertaintyinthetotal

φ

yielddue totheextrapolationinclassI(X)is1% (4.4%).Thereisno

extrap-olationuncertaintyforthedN

/

d y of K∗0. Varyingthefitfunction produces a negligible changein



pT forK∗0 _{andsuch variations}

are not included in the systematic uncertainties. The systematic uncertainties on the yield and



pT are obtained by varying the parametersusedinthedefaultanalysis.Toinvestigatewhetherthe changesintheyielddN

/

d y and



pTarecorrelatedbetween differ-entmultiplicity bins,the effectofchangingeach parameteris si-multaneouslyevaluatedforboththeminimumbiaseventclassand each individual multiplicity class. The multiplicity-correlated and uncorrelatedcomponentsofthesystematicuncertaintiesare sepa-rated,withthelatterbeingplottedasshadedboxesinFigs.2-5.

The meantransversemomenta



pTforK∗0 and

φ

are shown inFig.2asfunctionsof



dNch

/

d

η



|η|<0.5andcomparedwithother

ALICEmeasurementsandresultsfrommodelcalculations.The



pT

valuesin pp collisions at

√

s

=

7 TeV [8] and 13 TeVfollow ap-proximately the same trend. The



pT values of K∗0 _and

_φ

_rise

slightly faster as a function of



dNch

/

d

η



|η|<0.5 in pp collisions

than in p–Pb collisions for



dNch

/

d

η



|η|<0.5



5; the



pT values

Fig. 3. Mean transversemomentaforK∗0 _{andφarecomparedwiththoseforK}0 S, (anti)protons,



+ ,



−+ +,and



−+ +inppcollisionsat√s=13 TeVasa functionofdNch/ dη|η|<0.5[9,18].Thevaluesfor



+ inthelowestmultiplicity classandfor



−+ + areshiftedhorizontallyforvisibility.Barsrepresent statis-ticaluncertainties,openboxesrepresenttotalsystematicuncertainties,andshaded boxesshowthesystematicuncertaintiesthatareuncorrelatedbetweenmultiplicity classes.

collisions as discussed in [8,11]. The measured



pT values are compared withfive differentmodel calculations:PYTHIA6 (Peru-gia 2011tune) [69],PYTHIA8(Monash 2013tune,both withand withoutcolor reconnection) [70], EPOS-LHC [38],andDIPSY [33]. PYTHIA8withoutcolor reconnectionprovides an almost constant



pTas



dNch

/

d

η



|η|<0.5 increases; thisisa very different

behav-ior with respect to the trends measured by ALICEand given by the other model calculations. Turning color reconnection on in PYTHIA8 gives better qualitative agreement with the measure-ments,althoughthecalculationstillsomewhatunderestimatesthe



pTvaluesforhadronscontaining strange quarks(K0_S,K∗0,

φ

,



,



,and



) [9]. Color reconnectionin PYTHIA8introduces a flow-likeeffect,resultinginan increase in



pTvalueswithincreasing multiplicity without assuming the formation of a medium that couldflow [62].PYTHIA6provides agooddescriptionofthe



pT

valuesfor

φ

,butunderestimates



pTforK∗0_.The

_

_pTvalues

pre-dicted by EPOS-LHC are consistent withthe measured values for

φ

,butslightlybelowthevaluesforK∗0.Amongthemodelresults obtainedforthepresentwork,EPOS-LHCgivesthebestagreement withthemeasureddata.DIPSYgivesalargerincreasein



pTfrom low to high



dNch

/

d

η



|η|<0.5 than is actually observed; this

dis-crepancyisgreaterforthe

φ

andisalsoobservedforotherstrange hadrons [9].

Thevaluesof



pTforK∗0 and

φ

arecomparedwiththosefor K0_S, (anti)protons, andstrange baryonsin the same collision sys-tem in Fig. 3. In central A–A collisions, a mass ordering of the



pT values is observed; particles with similar masses(e.g., K∗0, p, and

φ

) have similar



pT [11,51]. This behavior has been in-terpretedasevidencethat radialflowcould bea dominantfactor in determining the shapes of hadron pT spectra in central A–A

collisions. However, this mass ordering breaks down for periph-eralPb–Pb collisions,aswell asp–Pbandppcollisions(see Fig.7 in [14] and measurementsreportedin [8,9,18]).Inppcollisionsat

√

s

=

13 TeV, the



pTvalues for K∗0 are greater than those for themoremassiveprotonand



forthesamemultiplicity classes. The



pTvaluesfor

φ

exceedthosefor



andevenapproachthose for



,despite the approximately 30% largermass of the



. This couldbeamanifestationofdifferencesbetweenthe pT spectraof

mesonsandbaryonsordifferentbehavior forresonances in com-parison tothe longer livedparticles. In [8], the Boltzmann-Gibbs blast-wave model was used to predict the pT spectra of

light-flavorhadronsbasedonacombinedfitof

π

±,K±,and(anti)proton

pT spectra.Thisstudy suggested that strange hadrons(K0S,



,



,

and



)andotherlight-flavorhadronsmightparticipateina

com-mon radial flow, even in pp collisions, but that K∗0 _and

_φ

_do

notfollowthiscommonradialexpansion(fordetailsofthisstudy, see [8]).The samebehavior could resultinthe violationofmass orderingfor



pTseenat

√

s

=

13 TeV.A deviationofthe



pT val-ues of short-lived resonances above the trend for other hadrons could inprinciplebeexplainedby re-scatteringofthe resonance-decaydaughtersduring thehadronicphaseofthecollision,which is expected to be most important at low pT [41]. However, the

strongestre-scatteringphenomenaoccurincentralA–Acollisions, where no deviationfrom mass ordering isobserved. In addition, such effects wouldbe strongerfor theshorterlived K∗0 thanfor the

φ

, which decays predominantly outside the hadronic phase (even incentralA–Acollisions)andshould beminimally affected byre-scattering.Ontheotherhand,theobservedviolationofmass ordering could be dueto differencesbetweenbaryon andmeson

pT spectra.Baryon-to-mesonratiossuchasp

/

π

and

/

K0Sare

ob-served [8,10] tobeenhancedatintermediatepT(

∼

3 GeV

/

c),even

in pp and p–Pbcollisions, while similar enhancement is not ob-served in meson-to-meson ratios like K

/

π

. Differences between baryons and mesons have also beenobserved inthe mT spectra

ofhadronsmeasuredatRHICenergies [76,77].FormT



1 GeV

/

c,

mesonmTspectrafollowonecommontrend,whilebaryonsfollow

a different, more steeply falling trend as a function of mT. Such

differencesbetweentheshapesofbaryonandmesonspectramay resultinmesonshavinglarger



pTvaluesthanbaryonswith com-parable masses.The breakdownofmassordering, with



pT

(

p

)



<



pT

(

K∗0

)



≈ 

pT

()



<



pT

(

φ)



≈ 

pT

()



,isa commonfeatureof

the modelsshowninFig.2.Thisbehaviormaybe aconsequence ofhadron productionviafragmentationathigh pT ormT;meson

formation requiresonlythe productionofa quark-antiquark pair, whilebaryonformationrequiresadiquark-antidiquarkpair [76].

The pT-integrated yields ofK∗0 and

φ

are showninFig. 4as

functionsof



dNch

/

d

η



|η|<0.5.Forbothparticles,dN

/

d y exhibitsan

approximatelylinearincreasewithincreasing



dNch

/

d

η



|η|<0.5.

Re-sultsforppcollisionsat

√

s

=

7and13 TeVandforp–Pbcollisions at

√

sNN

=

5.02 TeVfollowapproximatelythesametrends.This

in-dicates that,for a givenmultiplicity, K∗0 _and

_φ

_{productionrates}

do not depend on the collision system orenergy. Similar results are seenforstrangehadrons [9].ThedN

/

d y values arealso com-paredwiththoseobtainedfromthesamemodels studiedforthe discussion of



pT. Forthe K∗0, EPOS-LHC and PYTHIA8 without color reconnection give the best descriptions, the other PYTHIA calculations exhibit fair agreement with the measured data, and DIPSYtendstooverestimatetheK∗0yields.The

φ

yieldstendtobe slightlyoverestimatedbyEPOS-LHCandslightlyunderestimatedby DIPSY, while the PYTHIAcalculationsunderestimate the

φ

yields by about40%. The selectedPYTHIA tunes alsounderestimate the yields of



,



, and



by similar factors [9]. For thesebaryons, the EPOS-LHC description becomes less accurate withincreasing strangenesscontent;DIPSYdescribesthe



and



yieldswell,but underestimatestheyieldsof



[9].

The ratiosofthe pT-integratedparticleyieldsK∗0

/

K,

φ

/

π

,

φ

/

K,

and



/

φ

areshowninFig.5asfunctionsof



dNch

/

d

η



|η|<0.5[9,18].

Within their uncertainties the ratios in pp collisions at

√

s

=

7 and 13 TeV andin p–Pbcollisions at

√

sNN

=

5.02 TeVare

con-sistent for similar valuesof



dNch

/

d

η



|η|<0.5. There isa hintof a

decreaseinK∗0

/

K withincreasing



dNch

/

d

η



|η|<0.5inallthree

col-lisionsystems;forppcollisionsat

√

s

=

13 TeVtheK∗0

/

K ratioin thehighestmultiplicityclassisbelowthelow-multiplicityvalueat the2.3

σ

level(consideringonlythemultiplicity-uncorrelated un-certainties). ThedecreaseinK∗0

/

K incentralPb–Pbcollisions [11,

48,49] hasbeenattributedtore-scatteringoftheK∗0 _decay

prod-uctsinthehadronicphaseofthecollision [46].Itremainsanopen question whether a decreasein pp collisions could be caused by the same mechanism. EPOS-LHC provides the best description of theK∗0

_/

_{K ratioinppcollisionsat}

√

_s

₌

_{13 TeV.PYTHIAandDIPSY}

Fig. 4. pT-integrated yieldsdN/ d y ofK∗0(averageoftheparticleandantiparticle)andφasfunctionsofdNch/ dη|η|<0.5.Resultsareshownforppcollisionsat√s=13and 7 TeV [8],aswellasforp–Pbcollisionsat√sNN=5.02 TeV [11].Themeasurementsinppcollisionsat√s=13 TeVarealsocomparedwithvaluesfromcommonevent generators [33,38,69,70].Barsrepresentstatisticaluncertainties,openboxesrepresenttotalsystematicuncertainties,andshadedboxesshowthesystematicuncertaintiesthat areuncorrelatedbetweenmultiplicityclasses.

Fig. 5. Ratios of pT-integrated particle yieldsK∗0/K,φ/ π, φ/K,and



/ φ inpp collisionsat√s=13 TeVasfunctionsofdNch/ dη|η|<0.5[9,18].These measure-mentsarecomparedwithdatafromppcollisionsat√s=7 TeV [8],p–Pbcollisions at √sNN=5.02 TeV [11,13],and Pb–Pb collisionsat √sNN= 2.76 TeV [48,49]. Thewidths ofthe boxesfor pp collisions at √s=13 TeV andp–Pb collisions donotrepresenttheuncertaintiesofdNch/ dη|η|<0.5. Themeasurementsfor pp collisionsat√s=13 TeVarealsocomparedtoresultsfromcommonevent gener-ators [33,38,69,70] andaCanonicalStatisticalModelcalculation [8].

tendto overestimate the ratioforlarge multiplicities anddo not reproducetheapparentdecreasewithincreasing



dNch

/

d

η



|η|<0.5.

The

φ

/

π

ratiogradually increases fromthelowest-multiplicity ppcollisions to mid-central Pb–Pbcollisions. This ratiocompares theyields oftwomesonswithzeronetstrangeness,oneofwhich hashiddenstrangeness.The canonicalstatisticalmodel(CSM) [8] witha chemicalfreeze-outtemperatureof156 MeVpredicts that thisratio shouldhavelittledependenceon themultiplicity,since the

φ

wouldnot besubjectto canonicalsuppression. Theresults ofthe CSMcalculation are inconsistent with the observed trend ofthe

φ

/

π

ratio.Forppcollisions at

√

s

=

13 TeV, theincreasing trendofthe

φ

/

π

ratiois reproduced fairly wellby the EPOS-LHC andDIPSY models, while the PYTHIA calculations underestimate the magnitude of the ratio. The

φ

/

K ratio also follows a simi-lartrend in the threecollision systems.It is fairly constant as a

function of



dNch

/

d

η



|η|<0.5,although there is an apparent small

increase with



dNch

/

d

η



|η|<0.5 from the lowest multiplicities up

to



dNch

/

d

η



|η|<0.5

≈

400. EPOS-LHCsomewhat overestimates the

φ

/

K ratio,butisclosertothemeasuredvaluesthanPYTHIA,which significantlyunderestimates

φ

/

K.WhilePYTHIA6andDIPSY under-estimate the

φ

/

K ratio, both results exhibit small increases with increasing multiplicity, which isqualitatively similar to the mea-sured trend.The CSMcalculation does not describe thebehavior ofthemeasured

φ

/

K ratioforthe



dNch

/

d

η



|η|<0.5 rangespanned

bytheALICEppmeasurements.

In addition tocomparing the yields of

φ

topions and kaons, it may be instructive to compare



and

φ

. These two particles contain thesame numberofstrange valence (anti)quarks:

φ

isa s

¯

s boundstateand



contains twostrange valence quarks. How-ever,



would be subject to canonical suppression, unlike the strangeness-neutral

φ

. Fig. 5 also shows the



/

φ

ratio in pp, p–Pb, and Pb–Pb collisions. The ratio increases with increasing



dNch

/

d

η



|η|<0.5 for low-multiplicity collisions and is then fairly

constantforawiderangeofmultiplicities:fromppandp–Pb colli-sionsat



dNch

/

d

η



|η|<0.5

≈

7 tocentralPb–Pbcollisions.Thereisa

possiblesmallincreaseinthe



/

φ

ratiofrom



dNch

/

d

η



|η|<0.5

≈

7

tothe highest-multiplicityp–Pbcollisions,aswell asadifference on the 1.5

σ

level between the p–Pb and Pb–Pb measurements at



dNch

/

d

η



|η|<0.5

≈

50. Nevertheless, there is no clear increase

in the ratio for



dNch

/

d

η



|η|<0.5

≥

7. The decrease in



/

φ

with

decreasing



dNch

/

d

η



|η|<0.5 for low multiplicities could be

inter-pretedasevidenceofcanonicalsuppressioninsmallsystems;the canonical statistical model predicts a decrease in the



/

φ

ratio withdecreasing



dNch

/

d

η



|η|<0.5 thatisqualitativelysimilartothe

measured data.However, canonicalsuppression wouldalsoresult in an increase inthe

φ

/

K ratio withdecreasing



dNch

/

d

η



|η|<0.5,

which is not observed. Given that



and K havedifferent num-bersof strange valence (anti)quarks,it is expectedthat



would bemoreaffectedby canonicalsuppression [8].Itwillbe interest-ing to extend the study of the

φ

/

K ratio to lower multiplicities totest ifthereis anyincrease inthisratiodueto canonical sup-pressionofkaonyields.Themeasuredmultiplicityevolutionofthe



/

φ

and

φ

/

K ratios suggests that the

φ

meson behaves as if it had between 1 and 2 units of strangeness: i.e.,



is enhanced morethan

φ

,whichis(possibly)enhancedmorethanK.In addi-tion,thereareindicationsofincreasesinthep/

π

and

/

K0_S ratios withincreasing



dNch

/

d

η



|η|<0.5[8,9] whicharequalitatively

simi-lartotheincreasein



/

φ

,butsmallerinmagnitude.Thissuggests thatbaryon-mesondifferences(e.g.,baryonsuppressionormeson enhancement)mightbeacontributingfactor,butnottheonly rea-son,forthelow-multiplicitybehaviorofthe



/

φ

ratio.EPOS-LHC, which includes core-corona effects, gives an increasing trend in

Fig. 6. Ratios ofparticleyieldsK∗0_/K0

S and φ/K0S asfunctionsof pT [9] forlow(X) andhigh(II)multiplicity classes.Themiddlepanelsshow thedoubleratios: the measurementsinclassIIdividedbythoseinclassX.Thesignificanceofthedeviationsofthedoubleratiosfromunityisplottedinthelowerpanels,withdashedlines indicatingadeviationatthe3σ level.Barsrepresentthestatisticaluncertainties,whileboxesrepresentthepartofthesystematicuncertaintythatisuncorrelatedbetween multiplicityclassesIIandX.



/

φ

withincreasing



dNch

/

d

η



|η|<0.5, although the values ofthe

ratioanditsflatteningathighmultiplicityarenotparticularlywell described.Incontrast,PYTHIAgivesaconstantordecreasingvalue of



/

φ

withincreasing



dNch

/

d

η



|η|<0.5,whichisinconsistentwith

theobservedtrend.DIPSY,whichincludesropehadronization, de-scribes the



/

φ

ratio over a wide



dNch

/

d

η



|η|<0.5 range, only

failingtodescribethedecreaseintheratiowithdecreasing multi-plicityforthelowest



dNch

/

d

η



|η|<0.5values.

The pT dependence of the particle ratios K∗0

/

K0S and

φ

/

K0S

is shown in Fig. 6 for low and high multiplicity classes (X and II, respectively). Both ratios increase at low pT and saturate for pT



2

.

5 GeV

/

c;however,forpT



2

.

5 GeV

/

c theK∗0

/

K0_S and

φ

/

K0_S

ratiosinthehighmultiplicity class(II)arelessthaninthelowest multiplicityclass(X).Thisbehaviorisqualitativelyconsistentwith observationsin Pb–Pb collisions at

√

sNN

=

2.76 TeV [49], where

theK∗0

/

K and

φ

/

K ratiosatlow pT incentralcollisions arelower

comparedtoppcollisions.Thedecreaseinthelow-pT K∗0

/

K ratio

in central Pb–Pb collisions withrespect to pp collisions is larger thanthe decreaseinthe

φ

/

K ratio,which couldbe expecteddue to the presence of re-scattering effects. Toquantify the decrease intheseparticleratios inppcollisions at

√

s

=

13 TeV,the mid-dlepanels ofFig.6 showthe doubleratios: thehigh-multiplicity values divided by the low multiplicity values. The double ratios are consistent with unity for pT



2

.

5 GeV

/

c, which suggests a

commonevolutionofthe pTspectraforthesethreemesons.

How-everfor pT



2

.

5 GeV

/

c,thesuppressionoftheK∗0

/

K0S ratiofrom

low tohigh-multiplicitycollisions isgreater thanthesuppression ofthe

φ

/

K0

S ratio.Thisisquantified inthelower panelsofFig. 6,

wherethesignificanceofthedeviationsofthedoubleratiosfrom unity isshown. For pT

<

1

.

2 GeV

/

c,the K∗0

/

K0S double ratio

de-viates from unity by 4–6.6 times its standard deviation, while the

φ

/

K0

S double ratiodeviates from unityat aboutthe 3

σ

level

for 0

.

6

<

pT

<

1

.

4 GeV

/

c. This difference may be a hint of

re-scatteringinsmallcollisionsystems.

5. Conclusions

TheALICECollaborationhasreportedmeasurementsoftheK∗0

and

φ

mesons at midrapidity in pp collisions at

√

s

=

13 TeV in multiplicity classes. The results have many qualitative simi-larities to those reported for longer lived hadrons in the same collision system [9,18,19] and are consistent with previous mea-surements [8] ofK∗0 _and

_φ

_{in pp collisions at}

√

_s

₌

_{7 TeV.The}

slopes of the pT spectra of K∗0 and

φ

are observed to increase

with increasing multiplicity for pT



4 GeV

/

c, which is

qualita-tively similartothecollectiveradialexpansionobservedinPb–Pb collisions, butcan alsobe explained through color reconnection. In contrast, the shapes of the pT spectra are the same for all

multiplicity classes athigh pT. Both the pT-integratedyields and

the mean transverse momenta increase with increasing charged-particle multiplicity atmidrapidity, withapproximately linear in-creases for the yields. It appears that, for a given multiplicity value,theyieldsoftheseparticlesareindependentofcollision sys-temandenergy, whilethe



pT valuesfollowdifferenttrendsfor different collision systems. The mass ordering ofthe



pT values observed in central Pb–Pb collisions is violated in pp collisions, with the K∗0 and

φ

mesons having greater



pT than baryons with similar masses. The EPOS-LHC model describes the multi-plicity dependence of the yields and



pT fairly well for pp col-lisionsat

√

s

=

13 TeV.TherearehintsthattheyieldsofK∗0may be reduced, particularly at low pT and high multiplicity, by

re-scatteringofitsdecaydaughtersinashort-livedhadron-gasphase in pp collisions;similar behavior isobserved in Pb–Pb collisions. The

φ

/

π

ratio increaseswith increasing



dNch

/

d

η



|η|<0.5 and the

yields of the

φ

meson evolve similarly to particles with 1 and 2 units of open strangeness. The

φ

/

K and



/

φ

ratios are both fairly constant, exhibiting only slow increases over wide multi-plicity ranges, although the



/

φ

ratio decreases with decreasing



dNch

/

d

η



|η|<0.5forthelowestmultiplicityppandp–Pbcollisions.

Inhigh-multiplicityppandp–Pbcollisions,theseratiosreach val-uesobservedincentralPb–Pbcollisions.Thismultiplicityevolution isnotconsistentwithsimpledescriptionsofcanonicalsuppression, butisqualitativelydescribed bythe DIPSYmodel,whichincludes ropehadronizationeffects.Thesenewmeasurementsofthe

φ

pro-vide furtherconstraintsfortheoreticalmodelsofstrangeness pro-ductioninsmallcollisionsystems.

Declaration of competing interest

Theauthorsdeclarethattheyhavenoknowncompeting finan-cialinterestsorpersonalrelationshipsthatcouldhaveappearedto influencetheworkreportedinthispaper.

Acknowledgements

The ALICECollaboration would like to thank all its engineers andtechniciansfortheirinvaluablecontributionstothe construc-tion of the experiment and the CERN accelerator teams for the

outstandingperformance of the LHC complex. The ALICE Collab-oration gratefully acknowledges the resources and support pro-videdbyallGridcentresandtheWorldwideLHCComputingGrid (WLCG) collaboration. The ALICECollaboration acknowledges the followingfundingagenciesfortheir support inbuildingand run-ningtheALICEdetector:A. I.AlikhanyanNationalScience Labora-tory(YerevanPhysicsInstitute)Foundation (ANSL),State Commit-teeofScienceandWorldFederationofScientists(WFS), Armenia; Austrian Academy of Sciences, Austrian Science Fund (FWF): [M 2467-N36] and Nationalstiftung für Forschung, Technologie und Entwicklung,Austria;MinistryofCommunications andHigh Tech-nologies, National Nuclear Research Center, Azerbaijan; Conselho Nacionalde Desenvolvimento Científico e Tecnológico(CNPq), Fi-nanciadorade Estudos e Projetos(Finep),Fundação de Amparo à Pesquisado Estado de São Paulo (FAPESP)andUniversidade Fed-eraldoRioGrandedoSul(UFRGS),Brazil;MinistryofEducationof China(MOEC), MinistryofScience &Technology ofChina (MSTC) andNationalNatural Science Foundation of China (NSFC), China; Ministry of Science and Education and Croatian Science Foun-dation, Croatia; Centro de Aplicaciones Tecnológicas yDesarrollo Nuclear(CEADEN),Cubaenergía, Cuba;The MinistryofEducation, YouthandSports oftheCzechRepublic,CzechRepublic;The Dan-ishCouncilforIndependentResearchNaturalSciences,theVillum Fonden and Danish National Research Foundation (DNRF), Den-mark;HelsinkiInstitute ofPhysics (HIP),Finland; Commissariatà l’ÉnergieAtomique (CEA), Institut Nationalde Physique Nucléaire etde Physique des Particules (IN2P3) andCentre National de la Recherche Scientifique (CNRS) and Région des Pays de la Loire, France; Bundesministerium für Bildung und Forschung (BMBF) andGSIHelmholtzzentrumfürSchwerionenforschungGmbH, Ger-many;GeneralSecretariatforResearchandTechnology,Ministryof Education,Research andReligions,Greece; NationalResearch De-velopmentandInnovationOffice,Hungary;DepartmentofAtomic Energy, Government of India (DAE), Department of Science and Technology, Government of India (DST), University Grants Com-mission,GovernmentofIndia(UGC) andCouncil ofScientificand Industrial Research (CSIR), India; Indonesian Institute of Science, Indonesia;CentroFermi- MuseoStoricodellaFisicaeCentroStudi e Ricerche Enrico Fermi and Instituto Nazionale di Fisica Nucle-are (INFN),Italy; Institute for InnovativeScience andTechnology, Nagasaki Institute of Applied Science (IIST), Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and JapanSocietyforthePromotionofScience(JSPS)KAKENHI,Japan; Consejo Nacional de Ciencia y Tecnología (CONACYT), through FondodeCooperaciónInternacionalenCienciayTecnología (FON-CICYT)andDirecciónGeneralde Asuntosdel PersonalAcademico (DGAPA),Mexico; Nederlandse OrganisatievoorWetenschappelijk Onderzoek(NWO),Netherlands; The ResearchCouncil ofNorway, Norway; Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pakistan; Pontificia Uni-versidad Católicadel Perú, Peru; Ministry of Science and Higher EducationandNationalScience Centre,Poland;Korea Institute of ScienceandTechnology Information andNationalResearch Foun-dation of Korea (NRF), Republic of Korea; Ministry of Education andScientificResearch,InstituteofAtomicPhysicsandMinistryof ResearchandInnovationandInstituteofAtomicPhysics,Romania; Joint Institute for Nuclear Research (JINR), Ministry of Education andScience of the Russian Federation, National Research Centre KurchatovInstitute,RussianScienceFoundationandRussian Foun-dation forBasic Research, Russia; Ministry ofEducation, Science, ResearchandSportoftheSlovak Republic, Slovakia; National Re-searchFoundationofSouthAfrica,SouthAfrica; SwedishResearch Council (VR) and Knut and Alice Wallenberg Foundation (KAW), Sweden;EuropeanOrganizationforNuclearResearch,Switzerland; Suranaree University of Technology (SUT), National Science and TechnologyDevelopmentAgency(NSDTA)andOfficeoftheHigher

Education Commission under NRU project of Thailand, Thailand; Turkish Atomic EnergyAgency (TAEK), Turkey;NationalAcademy ofSciences ofUkraine, Ukraine;Science andTechnology Facilities Council (STFC), United Kingdom; National Science Foundation of theUnitedStatesofAmerica(NSF) andUnitedStatesDepartment of Energy, Office of Nuclear Physics (DOE NP), United States of America.

References

[1]ALICECollaboration,B.Abelev,etal.,Multi-particleazimuthalcorrelationsin p–PbandPb–PbcollisionsattheCERNLargeHadronCollider,Phys.Rev.C90 (2014)054901,arXiv:1406.2474.

[2]ALICECollaboration,S.Acharya,etal.,Investigationsofanisotropicflowusing multi-particleazimuthalcorrelationsinpp,p–Pb,Xe–Xe,andPb–Pbcollisions attheLHC,Phys.Rev.Lett.123(2019)142301,arXiv:1903.01790.

[3]CMSCollaboration,V.Khachatryan,etal.,Evidenceforcollectivityinpp colli-sionsattheLHC,Phys.Lett.B765(2017)193–220,arXiv:1606.06198. [4]ALICECollaboration,B.Abelev,etal.,Long-rangeangularcorrelations onthe

nearandawaysideinp–Pbcollisionsat√sNN=5.02TeV,Phys.Lett.B719

(2013)29–41,arXiv:1212.2001.

[5]CMSCollaboration,V.Khachatryan,etal.,Evidenceforcollectivemulti-particle correlationsinpPbcollisions,Phys.Rev.Lett.115(2015)012301,arXiv:1502. 05382.

[6]ATLAS Collaboration, G. Aad, et al., Observation of long-range elliptic anisotropiesin√s=13and2.76TeVppcollisionswiththeATLASdetector, Phys.Rev.Lett.116(2016)172301,arXiv:1509.04776.

[7]ATLAS Collaboration, M. Aaboud, et al., Measurement ofmulti-particle az-imuthalcorrelations inpp,p–Pband low-multiplicityPb–Pbcollisionswith theATLASdetector,Eur.Phys.J.C77(2017)428,arXiv:1705.04176. [8]ALICECollaboration,S.Acharya,etal.,Multiplicitydependenceoflight-flavor

hadron production inpp collisionsat √s= 7TeV,Phys. Rev.C99 (2019) 024906,arXiv:1807.11321.

[9]ALICE Collaboration, S. Acharya, et al., Multiplicity dependence of (multi-)strangehadronproductioninproton-protoncollisionsat√s=13 TeV, Eur.Phys.J.C80(2020)167,arXiv:1908.01861.

[10]ALICECollaboration, B.Abelev,etal.,Multiplicitydependenceofpion,kaon, protonandLambdaproductioninp–Pbcollisionsat√sNN=5.02TeV,Phys.

Lett.B728(2014)25–38,arXiv:1307.6796.

[11]ALICECollaboration,J.Adam,etal., ProductionofK∗(892)0_{and φ(1020)in}

p–Pbcollisionsat√sNN=5.02TeV,Eur.Phys.J.C76(2016)245,arXiv:1601.

07868.

[12]ALICE Collaboration, J. Adam, et al., Enhanced production of multi-strange hadrons in high-multiplicity proton-proton collisions, Nat. Phys. 13 (2017) 535–539,arXiv:1606.07424.

[13]ALICECollaboration,J.Adam,etal.,Multi-strangebaryonproductioninp–Pb collisionsat√sNN=5.02TeV,Phys.Lett.B758(2016)389–401,arXiv:1512.

07227.

[14]ALICECollaboration,D.Adamová,etal.,Productionof

(

1385)±and

(

1530)0

inp–Pbcollisionsat √sNN=5.02TeV,Eur.Phys.J.C77(2017)389,arXiv:

1701.07797.

[15]ALICE Collaboration, S. Acharya, et al., Multiplicity dependence of light (anti-)nucleiproductioninp–Pbcollisionsat√sNN=5.02TeV,Phys.Lett.B

800(2020)135043,arXiv:1906.03136.

[16]ALICE Collaboration, S. Acharya, et al., Multiplicity dependence of (anti-)deuteron production in pp collisions at √s= 7 TeV, Phys. Lett. B 794(2019)50–63,arXiv:1902.09290.

[17]ALICECollaboration,S.Acharya,etal.,Productionoflight-flavorhadronsinpp collisionsat√s=7 and√s=13 TeV,arXiv:2005.11120 [nucl-ex].

[18]ALICECollaboration,S.Acharya,etal.,Multiplicitydependenceofπ,K,andp productioninppcollisionsat√s=13 TeV,arXiv:2003.02394.

[19]ALICECollaboration,S.Acharya,etal.,(Anti-)deuteronproductioninpp colli-sionsat√s=13 TeV,arXiv:2003.03184.

[20]NA57Collaboration,F.Antinori,etal.,Enhancementofhyperonproductionat centralrapidityin158A GeV/c Pb–Pbcollisions,J. Phys.G32(2006)427–442, arXiv:nucl-ex/0601021.

[21]STARCollaboration,B.I.Abelev,etal.,Enhancedstrangebaryonproductionin Au+Aucollisionscomparedtop+p at√sNN=200GeV,Phys.Rev.C77(2008)

044908,arXiv:0705.2511.

[22]ALICECollaboration,B.Abelev,etal.,Multistrangebaryonproductionat mid-rapidity inPb–Pb collisions at √sNN= 2.76 TeV,Phys. Lett. B728 (2014)

216–227,arXiv:1307.5543,Phys.Lett.B734(2014)409–410(Erratum). [23]J.Cleymans,I.Kraus,H.Oeschler,K.Redlich,S.Wheaton,Statisticalmodel

pre-dictionsforparticleratiosat√sNN=5.5TeV,Phys.Rev.C74(2006)034903,

arXiv:hep-ph/0604237.

[24]A. Andronic, P. Braun-Munzinger, J. Stachel, Hadron production in central nucleus nucleuscollisionsat chemical freeze-out,Nucl.Phys. A 772(2006) 167–199,arXiv:nucl-th/0511071.